Exploring Absolute Value Equations

Mr. Allen introduces solving absolute value equations, demonstrating through examples how to isolate and solve them. He explains scenarios where solutions are fractions and when equations have no solutions due to negative results. The video covers handling coefficients outside absolute values and emphasizes understanding the nature of absolute values in equations.

What is the first step in solving an absolute value equation where the absolute value is already isolated?

• Add 5 to both sides

• Multiply both sides by 2

• Split the equation into two separate equations

• Combine like terms

If the absolute value of 2x + 3 equals 19, what are the two possible equations you can set up?

• 2x + 3 = 19 and 2x + 3 = 2

• 2x + 3 = 19 and 2x + 3 = -19

• 2x + 3 = 19 and 2x + 3 = 0

• 2x + 3 = 19 and 2x + 3 = 3

What should you do first if the absolute value is not isolated on one side of the equation?

• Multiply both sides by 2

• Divide both sides by 3

• Add or subtract terms to isolate the absolute value

• Combine like terms

When solving the equation |3x + 1| = 28, what are the two equations you should solve?

• 3x + 1 = 28 and 3x + 1 = 2

• 3x + 1 = 28 and 3x + 1 = 3

• 3x + 1 = 28 and 3x + 1 = 0

• 3x + 1 = 28 and 3x + 1 = -28

What is the first step when you have a coefficient in front of the absolute value?

• Distribute the coefficient

• Isolate the absolute value by dividing by the coefficient

• Subtract the coefficient from both sides

• Add the coefficient to both sides

In the equation 3|x - 6| = 12, what should you do after isolating the absolute value?

• Add 6 to both sides

• Subtract 6 from both sides

• Split the equation into two separate equations

• Multiply both sides by 3

What should you expect when solving absolute value equations that result in fractions?

• The solution is always incorrect

• Fractions are common and acceptable

• You need to multiply by 2 to clear the fraction

• The equation has no solution

If you get a fraction as a solution in an absolute value equation, what should you do?

• Ignore it and try another method

• Check if the fraction satisfies the original equation

• Multiply both sides by the denominator

• Add the fraction to both sides

Why can't an absolute value equation equal a negative number?

• Because it results in a complex number

• Because absolute values are always positive

• Because it violates the rules of algebra

• Because negative numbers are not real

What should you conclude if an absolute value equation equals a negative number?

• The equation has no solution

• The equation needs to be simplified further

• The equation has infinite solutions

• The equation has one solution